1 Answer
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For AES-128, you can start at any round, take a specific setting for that round key, and invert it to come up with the unique AES key that generates that round key

For AES-192, you can start at any round, take a specific setting for that round key (and 64 bits from the previous or next round), and invert it to come up with the unique AES key that generates those round key bits

For AES-256, you can start at any round, take a specific setting for that round key (and the 128 bits from the previous or next round), and invert it to come up with the unique AES key that generates those round key bits

Because that is a 1:1 mapping because the master key, and the 128/192/256 round key bits, then if the master key is selected uniformly, so must the round key bits be.